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The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost…
Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are…
Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…
This paper is concerned with the differential sensitivity analysis of variational inequalities in Banach spaces whose solution operators satisfy a generalized Lipschitz condition. We prove a sufficient criterion for the directional…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…
The paper starts with a concise description of the recently developed semismooth* Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…
We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the…
We obtain rates of convergence of numerical approximations of abstract linear parabolic evolution equations in Banach spaces. Our estimates extend known results from the literature of finite element approximations of parabolic equations to…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…
In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…
We propose a duality scheme for solving constrained nonsmooth and nonconvex optimization problems in a reflexive Banach space. We establish strong duality for a very general type of augmented Lagrangian, in which we assume a less…
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…
The aim of this paper in to introduce a large class of mappings, called {\it enriched Kannan mappings}, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for…
We study a class of quasi-variational inequality problems defined over infinite dimensional Banach space and deduce sufficient conditions for ensuring solutions to such problems under the upper semi-continuity and pseudomonotonicity…
A general device is proposed, which provides for extension of exponential inequalities for sums of independent real-valued random variables to those for martingales in the 2-smooth Banach spaces. This is used to obtain optimum bounds of the…
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…
In this work, we characterize the existence of solution for a certain variational inequality by means of a classical minimax theorem. In addition, we propose a numerical algorithm for the solution of an inverse problem associated with a…
The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In…